Scattering of topological surface-state carriers at steps on surfaces

The resistance across a step on ultrathin films of three different topological insulators, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, and ${\left({\mathrm{Bi}}_{1-x}{\mathrm{Pb}}_x\right)}_2{\mathrm{Te}}_3$, was measured through anisotropy in two-dimensional resistivity by using the in situ square four-point probe method in ultrahigh vacuum. The step resistance was much larger for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ than for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ in the range of 1–10 quintuple-layer thickness, due to the smaller critical thickness for isolation of topological surface states in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The transmission probability of carriers across a step is much higher for the bulk-insulating ${\left({\mathrm{Bi}}_{1-x}{\mathrm{Pb}}_x\right)}_2{\mathrm{Te}}_3$ than bulk-metallic ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, due to prevention of scattering of surface-state carriers into the bulk states. We were able to deduce microscopic information concerning the transmission probability at individual steps from the resistance data obtained macroscopically.

Figure 1

Typical morphology of a thin film (a) grown on a flat silicon substrate and (b) on a vicinal substrate. (c) Schematic illustration of Fermi surfaces and band dispersions of the topological insulators examined in this work. Red arrows indicate scattering paths from a TSS to a bulk state.

Figure 2

(a), (b) The dependences of S4PP resistance on the rotation angle $\theta$ at room temperature for 3 QL, 4 QL, and 5 QL thick ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111) films and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(111) films on vicinal substrates, respectively. The solid lines are fitting curves reproduced by Eq. (1). The inset in (b) shows an SEM image under the measurement with the tip number and the illustration of the definition of $\theta$. Atomic steps run horizontally in the image. (c), (d) The dependences of 2D electrical conductivity of the ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin film on their thicknesses. The solid lines are cubic to the thickness, drawn as guides to the eye. For both markers and lines, red and blue correspond to the cases parallel to and perpendicular to the atomic steps, respectively. (e), (f) The dependences of the conductivity anisotropy ${\sigma }_{\parallel }/{\sigma }_{\perp }$ of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ (red circles) and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (blue boxes) on the film thickness. (f) is the magnification of (e). The dashed lines are guides to the eye.

Figure 3

(a) The RHEED pattern of ${\left({\mathrm{Bi}}_{0.80}{\mathrm{Pb}}_{0.20}\right)}_2{\mathrm{Te}}_3$ 3 QL film. (b) The dependence of S4PP resistance of 3 QL ${\left({\mathrm{Bi}}_{0.80}{\mathrm{Pb}}_{0.20}\right)}_2{\mathrm{Te}}_3$ on the rotation angle $\theta$ measured at 6 K. (c) The temperature dependences of the resistivity of the 3 QL thick ${\left({\mathrm{Bi}}_{0.80}{\mathrm{Pb}}_{0.20}\right)}_2{\mathrm{Te}}_3$ thin film along (the red circles) and across (the blue triangles) the steps. (d), (e) Schematic illustrations of the electrical conduction in a vicinal topological insulator film with atomic steps (d) from the top view and (e) the side view. Equivalent circuits are overlapped.